### Woburn Challenge 2018-19 Round 4 - Junior Division

## Problem 3: Inventory

Billy, the king of video games, has received exclusive early access to play the upcoming action role-playing game *Diablo Immortal*! He's found that it truly revolutionizes the *Diablo* series, not only by moving to the superior gaming environment of a mobile phone, but by introducing a new system for managing the player's item inventory.

Billy has 1 or more items which he'd like his character to carry around, each of which has a certain size which indicates how many inventory slots it takes up. There are `A` size-1 items (which take up 1 inventory slot each), `B` size-2 items, and `C` size-3 items (0 ≤ `A`, `B`, `C` ≤ 1,000,000,000, 1 ≤ `A` + `B` + `C` ≤ 1,000,000,000).

The character isn't allowed to carry all of these items around directly, as that would be unrealistic. Instead, they must be packed into knapsacks. Each knapsack has 3 inventory slots, meaning that it can fit 1 or more items as long as the sum of their sizes is at most 3. Each item must be packed entirely into a single knapsack.

The character may carry any number of knapsacks, but each one must be purchased through an in-game microtransaction, so Billy would prefer to use as few as possible. Help him determine the minimum number of knapsacks required to fit all of the items!

### Subtasks

In test cases worth 16/28 of the points, `A` + `B` + `C` ≤ 100.

### Input Format

The first and only line of input consists of three space-separated integers, `A`, `B`, and `C`.

### Output Format

Output a single integer, the minimum number of knapsacks required.

### Sample Input 1

1 1 1

### Sample Output 1

2

### Sample Input 2

100 0 0

### Sample Output 2

34

### Sample Explanation

In the first case, Billy can fill one knapsack with both the size-1 and the size-2 items, and a second knapsack with the size-3 item.

In the second case, Billy can fill 33 knapsacks with 3 size-1 items each, and pack the single leftover size-1 item into a 34th knapsack.

All Submissions

Best Solutions

**Point Value:** 5 (partial)

**Time Limit:** 2.00s

**Memory Limit:** 16M

**Added:** Mar 22, 2019

**Author:** SourSpinach

**Languages Allowed:**

C++03, PAS, C, HASK, ASM, RUBY, PYTH2, JAVA, PHP, SCM, CAML, PERL, C#, C++11, PYTH3

## Comments (Search)

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